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22 February 2009

I have a question which is off-topic, but I was hoping for a suggestion. I'm doing an undergraduate statistics project, and I want to make mine climate change-oriented. I was hoping for some useful suggestions as to what would make a good idea-- I'm hoping of doing some kind of ice core data analysis (of some variable). My background in statistics is confined to a beginner class, but I do have math background out to differential equations and calc courses, so I can pick up.

I ask because stats in climate can get ugly pretty quick...principal component analysis and all that stuff is a bit beyond me. I still want something that is practical and informative. I can do the research in the climate literature and understand the terminogy; my barrier is moreso in data analysis background.

I'll throw this open also for ideas from readers. First step, I think, in a science project is to get a lot of ideas together.

Some good books to read for the statistics side of things are:How to Lie With Statistics by Darrell HuffLady Luck by Warren WeaverThe Visual Display of Information by Edward Tufte

On the ice core side:The Two Mile Time Machine by Richard AlleyIce Ages: Solving the Mystery by John and Katherine Palmer Imbrie

Most relevant to your specific thoughts is Alley's book. But read the others when you have time.

For projects ...Well, one part would be to start looking at the ice core literature and see what suggests itself. Starting with the Vostok ice cores from the mid-1980s there has been a lot of publication on these in Science and Nature (easy journals to get hold of). For doing this, it's good to think a bit about what kinds of analysis techniques you have from your stats class, and then see what has been published on that sort of analysis. While it's likely (but not guaranteed!) that the analysis has been done before, just not published, it's also possible that it hasn't been done.

I'd stay away from the more hard core time series analysis side of things here as this is your first stats class and the ice core time series are not on the more straightforward side of that problem.

But it should be doable to have a look at the ice cores for the 'climate' lengths of time in the way I was describing, casually, in how to decide climate trends and finding climate means. The ice cores have coarser resolution, but this is made up by the greater time spans they cover. An important part of the decision that I described in the means note is that if you go longer (than 30 years, in that case) new processes might start acting. In that case, you want some even longer averaging period -- long enough to average out those processes that are, say, 50-200 years long, and short enough to not be much affected by the ones 1500-2500 years long. But what is that period? Is it the same for all variables (CO2, Salt, dust, ...)? Is it the same for glacials and interglacials?

The hard core part of the project is to go beyond what I did, which was only eyeball verification. To do that, you want to find appropriate statistical tests to determine that, for instance, the mean as computed with a 300 year span of data is essentially the same (and what would 'essentially the same' mean in statistics?) as for 400 years, but both are meaningfully different from the means computed for 200 or 600 years.

Similarly, how can you tell that the means for glacial period are different than means for interglacials? Better, how can you determine objectively from the data just when the glacials and interglacials start and end?

Ice core data is archived at the National Geophysical Data Center. You'll also have to do some thinking about which data to use, how. The longest time series come from Antarctica, but they also have the worst time resolution. Better resolution comes from Greenland, but it's shorter. Better time resolution still comes from Andean and Himalayan glaciers, but they're much shorter.

The question of what are the climate periods in ice cores is an open one in the professional literature. At least as of fall 2007 when an ice core person was asking me how sea ice people selected their climate period, and I asked her about ice core people did.

Good luck on whatever version of project you do. And do let us know how it turns out!

9 comments:

Open Mind is definitely a good place to go look for ideas and illustrations. On the other hand, it's also a good place to go see why I suggested a first-time stats student stay away from time series analysis.

OT: Tsonis et al have published again and have some new scary-sounding results. I haven't seen the paper itself.

Another question has occurred to me:

Recent work (review article) has established that the tropics have been expanding and pushing the rest of the atmospheric circulation poleward. The most important obvious effect has been to accelerate the circular flow of air and water around Antarctica. This effect is apparently critical to the operation of the glacial cycles and is expected to continue into the future (as discussed here) as warming proceeds. The latter effect appears to be confirmed by these recent results. Analysis of flow in the Northern Hemisphere seems to be trickier, but is the circulation shift discussed in this new paper a related effect? Finally, the possibly related effect of a two-day phase change in the seasonal cycle is discussed in this paper.

I'd appreciate any thoughts you might have on all of this, Bob, but my specific question is whether the amount of energy needed to drive these effects could have anything to do with the recent relatively flat trend in global temperatures. In particular spinning up the Antarctic Circumpolar Current to a noticable extent sounds as if it would require a monumental amount of energy.

Of course all of this could relate back to what Tsonis et al are working on. The prior paper we discussed said in its conclusion that the anthropogenic temp trend could be overlaid on the hypothesized underlying cycle, but it seems to me that if increasing temps are pushing the entire circulation system out of shape that the underlying cycle would necessarily have to be perturbed. Perhaps the new paper addresses this point, though.

Steve (re: short comment): Sorry, I knocked that one out too quickly. I had meant to mention Open Mind myself. If Bart's class has done more on time series than is typical, he might be able to use that to move along to ice cores.

Longer comment: I'll take a look at the papers. In the mean time, I have very bad news for you. The amount of energy involved in the atmosphere's circulation (dynamics) is vastly less than the thermal energy of warming it up, and even less than warming up the ocean or melting ice.

Consider 1 kilogram of atmosphere. That's also about 1 cubit meter. If we make it move at 5 meters/second (a typical atmospheric wind speed), it has energy of 12.5 joules. To warm it by 1 degree (Celsius), we'll have to dump in about 1000 joules. 80x.

Now go to 1 kg of ocean (about 1 liter). To warm that by 1 C will require about 4000 joules. 320x. Worse, there's about 300 times as much mass in the ocean as atmosphere. Its energy reservoir or sink, per degree C, is therefore about 100,000 times as large as the entire atmosphere's.

Move on to ice and try to melt 1 kg (again about 1 liter) of it. That's going to take about 339,000 joules. About 85x warming a kg of ocean, and 6800x a kg of warming the atmosphere, by 1 C. There are about 4 times as many kg of ice as atmosphere, so this nets to about 27,000 times the energy sink as trying to warm the atmosphere by 1 degree.

The upshot of this is, it is extremely easy to bury energy in the oceans and ice, without seeing much of it appear as atmospheric temperature. It is also extremely easy to bury energy as atmospheric temperature rather than atmospheric dynamics. Conversely, the energy represented by atmospheric dynamics is absolutely trivial compared to air, sea, ice heating/cooling.

Barry Brooks at Brave New Climate has mentioned some about the division of where the energy is going, though I'm not finding the specific article at the moment. Still, if you haven't been reading him, do. Good stuff there.

Thanks for that detailed reply, Bob (and apologies for my belated response). There's no disappointment at all as I really wasn't expecting a Nobel out of that idea. :) Actually I still wonder a little about the amount of energy that's gone into spinning up the ACC, but that doesn't sound likely to be an explanation either.

Speaking again of Tsonis et al, see this rather sad post. The associated article is sketchy, but Swanson's remarks sound a bit bold.

I agree, Steve, that Swanson sounds a bit bold. But that doesn't mean he's wrong. Time to read him carefully in the scientific paper and see why he came to his conclusions. Right off, though, his estimate for how much warming we'd expect to have happened in the last few years seems quite high. Have to see how he got there.

Bart, good luck on the project and let us know how it goes. See also my Tuesday (coming) post as I encountered a site that made some elementary mistakes on CO2 and temperature.

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About Me

In my day job I work on the oceanography, meteorology, climatology, glaciology end of my science interests, but I'm interested in everything, science or not. So I've also been on stage in a production of Comedy of Errors, run an ultramarathon, and been to Epidaurus, Greece, to see a production of Euripides' Iphigenia among the Taurians
Prior to starting the current job, I was a post-doc in oceanography in the UCAR ocean modelling program, and earned my doctorate from the Department of the Geophysical Sciences at the University of Chicago (1989). My undergraduate degree involved Applied Math, Engineering, Astrophysics, and Glaciology.
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